[Ifeffit] Measuring particle size of metal oxide

[Scott Calvin]

Hi Bill,

Sorry for my slow response; I've been swamped. And ironically, the  
fact that I'm very interested in your topic and wanted to give a good  
reply slowed me from getting to it!

I'm also going to repost your question and my response to the IFEFFIT  
mailing list, as I think it's of general interest.

I think you're missing a key idea concerning this procedure. Both my  
method and Anatoly Frenkel's method for finding particle size rely on  
comparing the effective coordination for different paths. I am  
skeptical of EXAFS determinations of particle size using only one  
path, as coordination number is hard to tease out from other effects  
that suppress amplitude (sample quality, disorder, vacancies...). But  
the relative coordination number of different shells is more reliable.

So you should be using more than one path, each with its own r (the  
absorber-scatterer distance), in order to refine a single value for R,  
the crystallite radius.

If you're using Artemis, this is simple enough to do, as each path has  
a reff value (which is r in the formula you give), and you can define  
a guessed parameter R. (To do this right, you need to make sure that  
the r for multiple-scattering paths is the distance from the absorber  
to the furthest scatterer, not the half-path length. That means  
putting the value in "by hand" for those paths, rather than using reff.)

(If you want a really quick and dirty method, collect a reference for  
a bulk standard and for your sample, and multiply the FT of the bulk  
spectrum by the formula, adjusting R until you get a good match. The  
quick and dirty method doesn't handle multiple-scattering correctly,  
and has the usual problem of the fact that even for direct-scattering  
paths the peaks of the FT are shifted from actual absorber-scatterer  
distances. But it is model-free, which can be nice in some cases.)

By the way, the formula you've cited is derived for spherical  
particles. If they're kinda sorta spherical, it will still give a  
decent approximation and fit. But if the particles are needle-shaped  
or flat plates, then it doesn't work well. You either have to derive  
another formula, or look at Anatoly's papers, which have addressed a  
number of common morphologies.

So far, everything I've said applies to metals, and you asked about  
oxides. While most of this also applies to oxides, it's important to  
realize that the nearest-neighbor oxide paths are not suppressed at  
all; i.e. the formula doesn't apply until the first metal-metal path  
(but does apply to metal-oxide paths further out). This is because the  
surface of such particles is generally comprised of oxygen atoms, and  
the first scattering shell is thus fully populated no matter how small  
the particles are.

--Scott Calvin
Sarah Lawrence College

On Mar 8, 2010, at 1:45 PM, bill.schwartz at yale.edu wrote:

> Hi Scott,
>
> We met a couple of times at the EXAFS last two EXAFS workshops at  
> BNL, for relative beginners like me.
>
> I am attempting to determine the particle size of PdO particles  
> supported on Alumina (3% PdO/Al2O3).
>
> I am wondering if I can collect EXAFS data and use the formula in  
> your 2003 Journal of Applied Physics paper(*) to estimate PdO  
> particle size:
>
> N_nano = [1-3/4(r/R)+1/16(r/R)^3]N_bulk
>
> Here is a little more background:
>
> PdO particles on metal oxide supports are generally smaller and more  
> dispersed in comparison to Pd metal on the same support.  Also, if  
> PdO is reduced and then re-oxidized at varying temperatures, the re- 
> oxidized PdO particle size varies with temperature, with higher  
> oxidation temperatures resulting in smaller PdO particle size.
>
> I have prepared a series of samples of 3% PdO/Al2O3, where the PdO  
> has been been reduced and then re-oxideized at various temperatures,  
> and I would like to use EXAFS to determine the coordination number  
> of my various samples.
>
> A major difference in my planned experiment compared to what you  
> described in your paper is that you examined nickel metal, while I  
> am looking at a metal oxide.
>
> So my current questions are:
>
> 1)  Is the above formula reasonable for determining bulk particle  
> radius (R) of metal oxides?
>
> 2)  If yes, then what is r, since scattering distance between Pd -  
> Pd and Pd - O are different?  Is it reasonable to average the  
> distances?
>
> 3)  Can N(nano) be determined by averaging the coordination numbers  
> for the Pd-Pd and Pd-O paths?
>
> Any guidance you can provide will be greatly appreciated.
>
> Sincerely,
>
> Bill
>
> (*)  Determination of crystallite size in a magnetic nanocomposite  
> using extended x-ray absorption fine structure
>
>
>
>
>

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